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Wavepacket
In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating. Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation, and through its ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Packet (no Dispersion)
In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating. Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation, and through its ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Packet (dispersion)
In physics, a wave packet (or wave train) is a short "burst" or "envelope" of localized wave action that travels as a unit. A wave packet can be analyzed into, or can be synthesized from, an infinite set of component sinusoidal waves of different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere. Each component wave function, and hence the wave packet, are solutions of a wave equation. Depending on the wave equation, the wave packet's profile may remain constant (no dispersion, see figure) or it may change (dispersion) while propagating. Quantum mechanics ascribes a special significance to the wave packet; it is interpreted as a probability amplitude, its norm squared describing the probability density that a particle or particles in a particular state will be measured to have a given position or momentum. The wave equation is in this case the Schrödinger equation, and through its ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the ''spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (''ordinary frequency'') or radians per unit time (''angular frequency''). In multidimensional systems, the wavenumber is the magnitude of the ''wave vector''. The space of wave vectors is called ''reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the ''canonical momentum''. Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is often used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uncertainty Principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, ''x'', and momentum, ''p'', can be predicted from initial conditions. Such variable pairs are known as complementary variables or canonically conjugate variables; and, depending on interpretation, the uncertainty principle limits to what extent such conjugate properties maintain their approximate meaning, as the mathematical framework of quantum physics does not support the notion of simultaneously well-defined conjugate properties expressed by a single value. The uncertainty principle implies that it is in general not possible to predict the value of a quantity with arbitrary certainty, even if all initial conditions are specified. Introduced first in 1927 by the German physicist Werner ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Wavepacket Tunneling In Potential Well
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymous adjective ''Gaussian'' is pronounced . Mathematics Algebra and linear algebra Geometry and differential geometry Number theory Cyclotomic fields *Gaussian period *Gaussian rational *Gauss sum, an exponential sum over Dirichlet characters ** Elliptic Gauss sum, an analog of a Gauss sum **Quadratic Gauss sum Analysis, numerical analysis, vector calculus and calculus of variations Complex analysis and convex analysis *Gauss–Lucas theorem *Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions * Gauss's criterion – described oEncyclopedia of Mathematics* Gauss's hypergeometric theorem, an identity on hypergeometric series * Gauss plane Statistics *Gauss–Kuz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Afshar Experiment
The Afshar experiment is a variation of the double-slit experiment in quantum mechanics, devised and carried out by Shahriar Afshar while at the private, Boston-based Institute for Radiation-Induced Mass Studies (IRIMS). The results were presented at a Harvard seminar in March 2004. Afshar claimed that the experiment gives information about which of two paths a photon takes through the apparatus while simultaneously allowing interference between the two paths to be observed, by showing that a grid of wires, placed at the nodes of the interference pattern, does not alter the beams. Afshar claimed that the experiment violates the principle of complementarity of quantum mechanics, which states roughly that the particle and wave aspects of quantum objects cannot be observed at the same time, and specifically the Englert–Greenberger duality relation. The experiment has been repeated by a number of investigators, but its interpretation is controversial, and there are several the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Complementarity
In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously. An example of such a pair is position and momentum. Bohr considered one of the foundational truths of quantum mechanics to be the fact that setting up an experiment to measure one quantity of a pair, for instance the position of an electron, excludes the possibility of measuring the other, yet understanding both experiments is necessary to characterize the object under study. In Bohr's view, the behavior of atomic and subatomic objects cannot be separated from the measuring instruments that create the context in which the measured objects behave. Consequently, there is no "single picture" that unifies the results obtained in these different experimental contexts, and only the "totality of the phenom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ultraviolet Catastrophe
The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy as wavelength decreased into the ultraviolet range. The term "ultraviolet catastrophe" was first used in 1911 by Paul Ehrenfest, but the concept originated with the 1900 statistical derivation of the Rayleigh–Jeans law. The phrase refers to the fact that the Rayleigh–Jeans law accurately predicts experimental results at radiative frequencies below 100 THz, but begins to diverge from empirical observations as these frequencies reach the ultraviolet region of the electromagnetic spectrum. Since the first use of this term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence. Problem The Rayleigh-Jeans law is an approximation to the spectral radianc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always move at the speed of light in vacuum, (or about ). The photon belongs to the class of bosons. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality, their behavior featuring properties of both waves and particles. The modern photon concept originated during the first two decades of the 20th century with the work of Albert Einstein, who built upon the research of Max Planck. While trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, Planck proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain the photoelectric effect, Ein ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electricity and magnetism, two distinct but closely intertwined phenomena. In essence, electric forces occur between any two charged particles, causing an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs exclusively between ''moving'' charged particles. These two effects combine to create electromagnetic fields in the vicinity of charge particles, which can exert influence on other particles via the Lorentz force. At high energy, the weak force and electromagnetic force are unified as a single electroweak force. The electromagnetic force is responsible for many o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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